Aq-Analogue of Faà di Brunoʹs Formula

Some years ago Gessel ([Ge]) introduced aq-analogue of functional composition that was strong enough to support aq-analogue of the chain rule. In this note we show that Gesselʹsq-composition is even strong enough to support a-analogue of Faà di Brunoʹs formula for thenth derivative of a composite function.q-analogues of the Bell polynomials arise naturally in this context.